Computer geometric modelling is the mathematical representation of an object’s geometry using software. A geometric model contains description of the modelled object’s shape. Since geometric shapes are described by surfaces, curves are used to construct them. Computer geometric modelling uses curves to control the object’s surfaces as they are easy to manipulate. The curves may be constructed using analytic functions, a set of points, or other curves and surfaces. There are number of software programs that then allow the mathematical description of the object to be displayed as an image on the monitor.

A geometric model of an object can be created using these 3 steps:

Create basic geometric object using the commands like points, line and circles in CAD software

Use commands like achieve scaling, rotation, etc. to transform these geometric elements

Integrate the various elements of the object to form the final geometric model

A Bit of History…

In engineering, modelling refers to the way data are represented in the computer memory and the way in which it is visualized. The data is stored in a suitable data structure that is easy to access for the visualization algorithm. Geometric modelling is the process of capturing the properties of an object or a system using mathematical formulae. Computer geometric modelling is the field that discusses the mathematical methods behind the modelling of realistic objects for computer graphics and computer aided design. It uses computers to store the data and the geometric properties of a system / part. It is a relatively new technology that has expanded rapidly thanks to advances in computer technology. The 1st generation CAD programs of the 50’s were mostly non interactive. CAD users were required to create program codes to generate the desired 2D geometric shapes. Interactive CAD programs began to take shape in the 60’s and were mostly used in the automotive and the aerospace industry. The 60’s also marked the beginning of the development of finite element analysis methods for computer stress analysis and CAM for generating machine tool paths. The advent of microprocessors in the late 70’s boosted computing power of the computers. It also triggered the development of 3D CAD programs that were user friendly and most importantly, interactive. The 80’s saw the expansion of computer application software technology from very simple computer aided drafting to very complex computer aided design. It was at this time that 2D and 3D wire frames were introduced in the industry for geometric modelling as a tool to increase productivity.

During the process of geometric modeling the computer converts various commands given from within the CAD software into mathematical models, stores them as files and finally displays them as an image. The geometric models created by the designer can open at any time for reviewing, editing or analysis.

CAD really came on its own with the introduction of 3D solid modelling technology, which boosted the usage of CAE technology in industry. The development of 3D modelling schemes started with 3D wireframes. It was a major leap in computer geometric modeling as it allowed designers to use a single object and view it from multiple angles. However, wire frames are susceptible to ambiguity because surface definition is not part of a 3D wireframe model. To overcome this lacuna, computer geometric modelling with surface definitions was the next logical step forward. With enhanced computer CPU power, the next enhancement in geometric modelling was solid modelling. Surface modelling organizes and groups edges that define polygonal surfaces, making it easier for designers to visualize an object.

Solid Geometric Modelling

Solid modelling allows definition of an object’s nodes, edges and surfaces. It is therefore a complete and unambiguous mathematical representation of a precisely enclosed and filled volume. Unlike the surface modelling method, solid modellers start with a solid or use topology rules to guarantee that all surfaces are stitched together properly.

There are two predominant methods for representing solid models – constructive solid geometry and boundary representation. Constructive solid geometry combines basic solid objects (for example a rectangular prism, cylinder, cone, sphere, etc.). These shapes are simply added or deleted in order to form the final solid shape. In boundary representation, objects are defined in terms of their spatial boundaries. It defines the points, edges, surfaces of a volume, and / or issues commands that sweep or rotate a defined face into a third dimension to form a solid. The object is then made up of the union of these surfaces that completely and precisely enclose a volume.

The 80’s also saw a new paradigm called concurrent engineering. In this concept, the entire production team (designers, analysts, engineers, testers and production managers) work concurrently right from the inception of the project. Feature based parametric modelling is the result of this collaboration; we have covered it separately.

To summarize, these are the various types of computer geometric modeling techniques as of date:

Wire frame models (describe an object using boundary lines)

Surface models (describe an object using boundary surfaces)

Solid models (describe an object as a solid)

The Kernel and its Importance

Solid geometric modelling has grown in popularity. It is one of the most important applications of CAD. CAD programs that use solid modelling concept help design engineers to view the part / object as if it was really manufactured. The CAD software can even change the perspective and viewing angles. SolidWorks, CATIA and PTC Creo are a few popular tools used for computer geometric modelling – especially solid modelling.

The heart of computer geometric modelling software is the kernel. Called either a geometric modelling kernel or solid modelling kernel, it is the code that determines how the image you see on the screen is actually described with math. Kernels are important because they are mathematical models of real and theoretical objects. Describing shapes in a mathematical representation involves making choices about how each shape is calculated and stored. Needless to say, the better a kernel, the better a geometric modelling software. In addition to all the functions required by programmers, a good kernel should also be reliable and quick. As the quality of a kernel affects the quality of the entire CAD system companies like PTC, SolidWorks, CATIA and others constantly strive to improve it.

Computer Geometric Modelling – the Future

Computer geometric modelling finds use in numerous sectors like industrial engineering, automotive engineering, aerospace, defence, power, etc. In addition, geometric modelling is also finding uses in many newer industries like robotics, medical imaging, visualization, etc. Developing countries (like India, China and Brazil for example) have seen a tremendous growth in the demand for companies that provide geometric modelling – solid as well as feature based. This is because simulation is typically time consuming. Unless you have state of the art software like PTC Creo, SolidWorks or CATIA - which small companies typically do not have - it is tedious as well. There have been cases where the geometric modelling time itself took about half the PLM time due to the complexity of the geometry! The more intricate the surface details (surface mesh), the better it is for design engineers. Companies that provide geometric modeling as a service are therefore growing in popularity in India and elsewhere.